Geodesic
Comparison of TVD and WENO schemes in the case of wave packet transport and vortex numerical diffusion problems
Matematičeskoe modelirovanie, Tome 23 (2011) no. 11, pp. 99-110

Voir la notice de l'article provenant de la source Math-Net.Ru

In the given paper, dissipative properties of TVD and WENO schemes are tested and compared. A brief review of limiters used in TVD schemes is presented. An iterative procedure of limiting minmod reconstruction is described. A procedure of WENO-reconstruction inside the cell for uniform grids is presented. For the test cases, a problem of wave packet transport and a problem of numerical diffusion of vortices are used. A problem of wave packet transport is solved for uniform and non-uniform grids. On the basis of comparison of theoretical and numerical solutions, dissipative properties of different limiters for TVD scheme and WENO scheme are estimated.
Keywords: TVD, limiting reconstruction, WENO
Mots-clés : transport equation, vortex, Euler equations. 
@article{MM_2011_23_11_a6,
     author = {S. V. Mikhailov and A. A. Savelyev},
     title = {Comparison of {TVD} and {WENO} schemes in the case of wave packet transport and vortex numerical diffusion problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {99--110},
     publisher = {mathdoc},
     volume = {23},
     number = {11},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_11_a6/}
}
TY  - JOUR
AU  - S. V. Mikhailov
AU  - A. A. Savelyev
TI  - Comparison of TVD and WENO schemes in the case of wave packet transport and vortex numerical diffusion problems
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 99
EP  - 110
VL  - 23
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_11_a6/
LA  - ru
ID  - MM_2011_23_11_a6
ER  - 
%0 Journal Article
%A S. V. Mikhailov
%A A. A. Savelyev
%T Comparison of TVD and WENO schemes in the case of wave packet transport and vortex numerical diffusion problems
%J Matematičeskoe modelirovanie
%D 2011
%P 99-110
%V 23
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_11_a6/
%G ru
%F MM_2011_23_11_a6
S. V. Mikhailov; A. A. Savelyev. Comparison of TVD and WENO schemes in the case of wave packet transport and vortex numerical diffusion problems. Matematičeskoe modelirovanie, Tome 23 (2011) no. 11, pp. 99-110. http://geodesic.mathdoc.fr/item/MM_2011_23_11_a6/